Modified Bases of PHT-Splines

Abstract

Recently, it was found that during the process of certain refinement of hierarchical T-meshes, some basis functions of PHT-splines decay severely, which is not expected in solving numerical PDEs and in least square data fitting since the matrices assembled by these basis functions are likely to be ill-conditioned. In this paper, we present a method to modify the basis functions of PHT-splines in the case that the supports of the original truncated basis functions are rectangular domains to overcome the decay problem. The modified basis functions preserve the same nice properties of the original PHT-spline basis functions such as partition of unity, local support, linear independency. Numerical examples show that the modified basis functions can greatly decrease the condition numbers of the stiffness matrices assembled in solving Poisson’s equation with Dirichlet boundary conditions.

Keywords

PHT-spline / B-spline / Hierarchical T-mesh / Poisson’s equation

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Funding

National Natural Science Foundation of China(NO. 11571338)

Postdoctoral Science Foundation of China(2015M571931)